MAS8384 : Bayesian Methodology
- Offered for Year: 2019/20
- Module Leader(s): Dr Sarah Heaps
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
|Semester 2 Credit Value:||10|
Bayesian inference provides an ideal approach for synthesizing information from different sources in a coherent way. In recent years great advances have been made in the application of Bayesian statistical inference to problems across a wide variety of areas within industry, such as drug development, voice recognition and credit card fraud detection. This has been made possible by the development of computational algorithms which allow posterior distributions to be found in complicated models. This module starts with an introduction to the principles of Bayesian inference before moving on to address the fundamental practical problem of calculating the posterior distribution for complex models. The theory behind some modern Bayesian computational methods, which provide a simulation-based solution, is developed and put into practice using R.
Specifically, the module aims to equip students with the following knowledge and skills:
- To gain an understanding of the principles of the Bayesian approach to inference and experience in the application of Bayes rule to update a prior distribution to a posterior distribution using a likelihood function.
- To gain an understanding of the theory behind some modern Bayesian computational methods for approximating a posterior distribution and practical experience of their application in R to solve a variety of applied problems.
Outline Of Syllabus
- Conjugate Bayesian inference
- Non-conjugate models
- Markov chain Monte Carlo (MCMC): methods such as Gibbs sampling, Metropolis-Hastings sampling, slice sampling; assessment of mixing and convergence
- Posterior summaries
- Applications, such as linear models, generalized linear models, mixture models, hidden Markov models, dynamic linear models, Gaussian process regression
- Computation using R and R packages such as rjags
|Guided Independent Study||Assessment preparation and completion||1||0:30||0:30||Oral Examination|
|Guided Independent Study||Assessment preparation and completion||5||0:30||2:30||Preparation for oral examination|
|Guided Independent Study||Assessment preparation and completion||15||1:00||15:00||Completing Practical Reports|
|Scheduled Learning And Teaching Activities||Lecture||12||2:00||24:00||Lectures|
|Guided Independent Study||Directed research and reading||16||1:00||16:00||Background reading|
|Scheduled Learning And Teaching Activities||Practical||6||2:00||12:00||Practical Sessions|
|Guided Independent Study||Project work||21||1:00||21:00||Completing Project|
|Guided Independent Study||Independent study||9||1:00||9:00||Lecture follow-up (working through lecture notes)|
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Practicals are used both for solution of problems and work requiring extensive computation and to give insight into the ideas/methods studied; they are also used to discuss the course material, identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. The project allows the students to develop their problem solving techniques and practise the methods learnt in the module.
The format of resits will be determined by the Board of Examiners
|Practical/lab report||2||M||45||Up to 3, equally weighted, practical reports (15% each) 1000 words per report|
|Report||2||M||55||Project report (up to 1500 words)|
Zero Weighted Pass/Fail Assessments
|Oral Presentation||M||A structured discussion including a software demonstration and reflection on the key learning objectives of the coursework project|
Assessment Rationale And Relationship
Written assignments (3 pieces of work of equal weight) followed by a larger piece of project work allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback.
The semi-structured oral examination facilitates a reflective discussion about how individual students have met the learning objectives of the module and how the principles of fundamental statistics are embedded in the functionality of their project work.